Question: What is the greatest common factor of $60w$, $36w^{2}$, and $24w^{4}$ ?
Answer: Let's factor each monomial to its prime factors: $\begin{aligned} 60w&=(2)(2)(3)(5)(w) \\\\ 36w^{2}&=(2)(2)(3)(3)(w)(w) \\\\ 24w^{4}&=(2)(2)(2)(3)(w)(w)(w)(w) \end{aligned}$ We want the largest set of factors that's included in all three monomials. All of the monomials have two factors of $ 2$, one factor of $ 3$, and one factor of $ w$ : $\begin{aligned} 60w&=( 2)( 2)( 3)(5)( w) \\\\ 36w^{2}&=( 2)( 2)( 3)(3)( w)(w) \\\\ 24w^{4}&=( 2)( 2)(2)( 3)( w)(w)(w)(w) \end{aligned}$ This is the greatest common factor: $( 2)( 2)( 3)( w)=12w$